On the geometry of p-origamis and beyond

The main topic of this thesis is the study of a special class of translation surfaces called normal origamis. The theory of translation surfaces is an active research area with applications in various fields such as dynamical systems, algebraic geometry, and geometric group theory. Normal origamis are surfaces with a maximal symmetry group and induce normal covers of the torus T. We focus on p-origamis, where the deck transformation groups of the torus covers are p-groups, and answer the questions: Which strata contain p-origamis? Does already the deck transformation group determine the stratum? We then turn toward the study of Veech groups of certain normal origamis. These groups are the stabilizer groups of an origami under an SL(2,Z)-action. We are especially interested in the question, whether the occurring Veech groups are congruence groups. The SL(2,Z)-orbits on normal origamis are closely related to the group-theoretic concept of T_2-systems. We investigate this relationship and transfer group-theoretic results to the geometric setting. Cylinder decompositions are an important concept occurring in different contexts within this thesis. Geminal origamis exhibit special cylinder decompositions. Apisa and Wright asked whether geminal origamis are cyclic covers of the surface (2 x 2)-torus. We use methods from group theory to answer this question partially. This thesis contains results of the author's research articles [FT20] and [The21].Im Zentrum dieser Dissertation steht das Studium normaler Origamis, einer Familie von Translationsflächen. Seit 40 Jahren sind Translationsflächen Gegenstand aktiver mathematischer Forschung mit Anwendungen in diversen mathematischen Bereichen wie algebraischer Geometrie und geometrischer Gruppentheorie. Normale Origamis haben eine maximale Symmetriegruppe und definieren normale Überlagerungen des Torus. Zunächst untersuchen wir p-Origamis, d.h. normale Origamis mit einer p-Gruppe als Decktransformationsgruppe. Wir beantworten die Fragen, welche Strata p-Origamis enthalten und ob die Decktransformationsgruppe bereits das Stratum festlegt. Des Weiteren betrachten wir Veechgruppen bestimmter normaler Origamis. Diese Gruppen sind Stabilisatoren eines Origamis unter einer SL(2,Z)-Wirkung. Unter anderem untersuchen wir die Fragen, ob und wann die Veechgruppen normaler Origamis Kongruenzgruppen sind. Zudem diskutieren wir den Zusammenhang zwischen den SL(2,Z)-Bahnen normaler Origamis und dem gruppentheoretischen Konzept der T_2-Systeme. Zylinderzerlegungen sind ein wichtiges Konzept in der Theorie der Translationsflächen, welches wir an verschiedenen Stellen in dieser Arbeit verwenden. Geminale Origamis sind Origamis mit sehr speziellen Zylinderzerlegungen. Unter gewissen Voraussetzungen beantworten wir die Frage, ob geminale Origamis den (2 x 2)-Torus zyklisch überlagern. Diese Dissertation enthält Ergebnisse aus folgenden Publikationen der Autorin [FT20] und [The21].German Research Foundation (DFG): SFB-TRR 195 Symbolic Tools in Mathematics and their Application

Annual banned-substance review: Analytical approaches in human sports drug testing 2019/2020.

Analytical chemistry-based research in sports drug testing has been a dynamic endeavor for several decades, with technology-driven innovations continuously contributing to significant improvements in various regards including analytical sensitivity, comprehensiveness of target analytes, differentiation of natural/endogenous substances from structurally identical but synthetically derived compounds, assessment of alternative matrices for doping control purposes, and so forth. The resulting breadth of tools being investigated and developed by anti-doping researchers has allowed to substantially improve anti-doping programs and data interpretation in general. Additionally, these outcomes have been an extremely valuable pledge for routine doping controls during the unprecedented global health crisis that severely affected established sports drug testing strategies. In this edition of the annual banned-substance review, literature on recent developments in anti-doping published between October 2019 and September 2020 is summarized and discussed, particularly focusing on human doping controls and potential applications of new testing strategies to substances and methods of doping specified the World Anti-Doping Agency's 2020 Prohibited List

A multivariate Bayesian learning approach for improved detection of doping in athletes using urinary steroid profiles

Biomarker analysis of athletes' urinary steroid profiles is crucial for the success of anti-doping efforts. Current statistical analysis methods generate personalised limits for each athlete based on univariate modelling of longitudinal biomarker values from the urinary steroid profile. However, simultaneous modelling of multiple biomarkers has the potential to further enhance abnormality detection. In this study, we propose a multivariate Bayesian adaptive model for longitudinal data analysis, which extends the established single-biomarker model in forensic toxicology. The proposed approach employs Markov chain Monte Carlo sampling methods and addresses the scarcity of confirmed abnormal values through a one-class classification algorithm. By adapting decision boundaries as new measurements are obtained, the model provides robust and personalised detection thresholds for each athlete. We tested the proposed approach on a database of 229 athletes which includes longitudinal steroid profiles classified as normal, atypical, or confirmed abnormal. Our results demonstrate improved detection performance, highlighting the potential value of a multivariate approach in doping detection.Comment: 25 pages, main manuscript pgs. 1-19, appendix A pgs. 19-22, appendix B pgs. 23-2

Combination of carbon isotope ratio with hydrogen isotope ratio determinations in sports drug testing

Carbon isotope ratio (CIR) analysis has been routinely and successfully applied to doping control analysis for many years to uncover the misuse of endogenous steroids such as testosterone. Over the years, several challenges and limitations of this approach became apparent, e.g., the influence of inadequate chromatographic separation on CIR values or the emergence of steroid preparations comprising identical CIRs as endogenous steroids. While the latter has been addressed recently by the implementation of hydrogen isotope ratios (HIR), an improved sample preparation for CIR avoiding co-eluting compounds is presented herein together with newly established reference values of those endogenous steroids being relevant for doping controls. From the fraction of glucuronidated steroids 5β-pregnane-3α,20α-diol, 5α-androst-16-en-3α-ol, 3α-Hydroxy-5β-androstane-11,17-dione, 3α-hydroxy-5α-androstan-17-one (ANDRO), 3α-hydroxy-5β-androstan-17-one (ETIO), 3β-hydroxy-androst-5-en-17-one (DHEA), 5α- and 5β-androstane-3α,17β-diol (5aDIOL and 5bDIOL), 17β-hydroxy-androst-4-en-3-one and 17α-hydroxy-androst-4-en-3-one were included. In addition, sulfate conjugates of ANDRO, ETIO, DHEA, 3β-hydroxy-5α-androstan-17-one plus 17α- and androst-5-ene-3β,17β-diol were considered and analyzed after acidic solvolysis. The results obtained for the reference population encompassing n = 67 males and females confirmed earlier findings regarding factors influencing endogenous CIR. Variations in sample preparation influenced CIR measurements especially for 5aDIOL and 5bDIOL, the most valuable steroidal analytes for the detection of testosterone misuse. Earlier investigations on the HIR of the same reference population enabled the evaluation of combined measurements of CIR and HIR and its usefulness regarding both steroid metabolism studies and doping control analysis. The combination of both stable isotopes would allow for lower reference limits providing the same statistical power and certainty to distinguish between the endo- or exogenous origin of a urinary steroi

Simplified quantification of insulin, its synthetic analogs and C-peptide in human plasma by means of LC-HRMS.

The quantification of peptide hormones by means of liquid chromatography (LC) coupled to mass spectrometry (MS) or other techniques (e.g. immunoassays) has been a challenging task in modern analytical chemistry. Especially for insulin, its synthetic analogs, and C-peptide, reliable determinations are urgently needed due to their diagnostic value in the management of diabetes and insulin resistance and because of the illicit use of insulin as a performance-enhancing agent in professional sports or as an effective toxin in forensic toxicology. The concomitant measurement of C-peptide and insulin offers an established tool for the diagnostic workup of hypoglycemia (endogenous vs. exogenous hyperinsulinemia), characterizing hepatic insulin clearance, and the assessment of beta-cell function (insulin secretion). Thus, the present approach offers the possibility to determine human insulin and its synthetic analogs (lispro, glulisine, aspart, glargine metabolite, degludec, detemir, porcine, and bovine) and C-peptide simultaneously after sample preparation utilizing protein precipitation and a mixed-mode cation-exchange solid-phase extraction, and subsequent detection by LC-high resolution MS. The method was fully validated regarding the following parameters: specificity, limit of detection (0.2 ng/mL), limit of quantification (0.6 ng/mL), recovery (40-90%), accuracy (78-128%), linearity, precision (< 21%), carry over, robustness, and matrix effects. The proof-of-concept was shown by analyzing authentic plasma samples from adults with class II obesity and prediabetes collected in the course of an oral glucose tolerance test. All sample preparation steps were controlled by two stable isotope-labeled internal standards, namely [[2 H10 ] Leu B6, B11, B15, B17 ]-insulin, and [[13 C6 ] Leu 26, 30 ] C-peptide

Effect of changes in the deuterium content of drinking water on the hydrogen isotope ratio of urinary steroids in the context of sports drug testing

The hydrogen isotope ratio (HIR) of body water and, therefore, of all endogenously synthesized compounds in humans, is mainly affected by the HIR of ingested drinking water. As a consequence, the entire organism and all of its synthesized substrates will reflect alterations in the isotope ratio of drinking water, which depends on the duration of exposure. To investigate the effect of this change on endogenous urinary steroids relevant to doping-control analysis the hydrogen isotope composition of potable water was suddenly enriched from -50 to 200 ‰ and maintained at this level for two weeks for two individuals. The steroids under investigation were 5β-pregnane-3α,20α-diol, 5α-androst-16-en-3α-ol, 3α-hydroxy-5α-androstan-17-one (ANDRO), 3α-hydroxy-5β-androstan-17-one (ETIO), 5α-androstane-3α,17β-diol, and 5β-androstane-3α,17β-diol (excreted as glucuronides) and ETIO, ANDRO and 3β-hydroxyandrost-5-en-17-one (excreted as sulfates). The HIR of body water was estimated by determination of the HIR of total native urine, to trace the induced changes. The hydrogen in steroids is partly derived from the total amount of body water and cholesterol-enrichment could be calculated by use of these data. Although the sum of changes in the isotopic composition of body water was 150 ‰, shifts of approximately 30 ‰ were observed for urinary steroids. Parallel enrichment in their HIR was observed for most of the steroids, and none of the differences between the HIR of individual steroids was elevated beyond recently established thresholds. This finding is important to sports drug testing because it supports the intended use of this novel and complementary methodology even in cases where athletes have drunk water of different HIR, a plausible and, presumably, inevitable scenario while travelin

Rational approximations, multidimensional continued fractions and lattice reduction

We first survey the current state of the art concerning the dynamical properties of multidimensional continued fraction algorithms defined dynamically as piecewise fractional maps and compare them with algorithms based on lattice reduction. We discuss their convergence properties and the quality of the rational approximation, and stress the interest for these algorithms to be obtained by iterating dynamical systems. We then focus on an algorithm based on the classical Jacobi--Perron algorithm involving the nearest integer part. We describe its Markov properties and we suggest a possible procedure for proving the existence of a finite ergodic invariant measure absolutely continuous with respect to Lebesgue measure.Comment: 30 pages, 4 figure

Do dried blood spots have the potential to support result management processes in routine sports drug testing?—Part 3: LC–MS/MS‐based peptide analysis for dried blood spot sampling time point estimation

Along with the recent acknowledgement of the World Anti-Doping Agency to use dried blood spot (DBS) samples for routine doping control purposes, there have been propositions to use DBS as a matrix that allows regular proactive remotely supervised self-sampling, providing potential longitudinal monitoring of an athlete's exposure to doping agents. However, several organizational aspects have to be considered before implementation, such as the verification of the sample collections time point. Based on a previous untargeted proteomics workflow utilizing liquid chromatography–high-resolution mass spectrometry (LC–HRMS) to identify protein/peptide markers to define the time since deposition of a bloodstain, the aim of the current study was to develop a targeted LC–HRMS/MS analytical method for promising peptidic target analytes. A long-term DBS storage experiment was carried out over a 3-month period (sample collection time points: 0, 2, 4, 7, 14, 21, 28, 42, 56, 70, 84 and 91 days) with DBS samples of 10 volunteers for longitudinal investigation of signal abundance changes of targeted peptide sequences at different storage temperatures (room temperature [RT], 4°C and −20°C). Prior to experimental analysis, LC–HRMS/MS method characteristics were successfully assessed, including intraday precision, carryover and sample extract stability. For estimation of DBS sample collection time points, ratios of two peptides that originate from the same protein prior to tryptic digestion were created. Two targeted peptide area ratios were found to significantly increase after being stored at RT for 28 days, representing potential markers for future use in routine doping controls that contribute to advancing complementary avenues in anti-doping

Acute hypertrophic but not maximal strength loading transiently enhances the kynurenine pathway towards kynurenic acid

Purpose Due to distinct immuno- and neuro-modulatory properties, growing research interest focuses on exercise-induced alterations of the kynurenine (KYN) pathway in healthy and clinical populations. To date, knowledge about the impact of different acute strength exercise modalities on the KYN pathway is scarce. Therefore, we investigated the acute effects of hypertrophic (HYP) compared to maximal (MAX) strength loadings on the KYN pathway regulation. Methods Blood samples of twelve healthy males (mean age and weight: 23.5 ± 3.2 years; 77.5 ± 7.5 kg) were collected before (T0), immediately after (T1), and 1 h after completion (T2) of HYP (5 sets with 10 repetitions at 80% of 1RM) and MAX (15 sets with 1RM) loadings performed in a randomized cross-over design. Serum concentrations of tryptophan (TRP), KYN, kynurenic acid (KA), and quinolinic acid (QA) were assessed using high-performance liquid chromatography. Results The KA/KYN ratio increased from T0 to T1 (p = 0.01) and decreased from T1 to T2 (p = 0.011) in HYP, while it was maintained within MAX. Compared to MAX, serum concentrations of KA were greater in HYP at T1 (p = 0.014). Moreover, the QA/KA ratio was significantly lower in HYP than in MAX at T1 (p = 0.002). Conclusion Acute HYP loading led to increases in the metabolic flux yielding KA, thereby possibly promoting immunosuppression and neuroprotection. Our findings emphasize the potential of acute HYP exercise as short-term modulator of KYN pathway downstream to KA in healthy males and need to be proven in other samples